Problem: Find: $\frac{12}{30}-\frac{1}{7}$
Answer: Because the first term of the expression, 12/30, is not simplified, we simplify before continuing, \[
\frac{12}{30} = \frac{6}{6}\cdot\frac{2}{5} = 1\cdot\frac{2}{5} = \frac{2}{5}.
\]However, the two terms have different denominators, so we have to find a common denominator, \[
\frac{2}{5} - \frac{1}{7} = \frac{2}{5} \cdot \frac{7}{7} - \frac{1}{7} \cdot \frac{5}{5} = \frac{14}{35} - \frac{5}{35} = \boxed{\frac{9}{35}}.
\]The answer is in simplest form.